The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
Interpretation
Ideas flourish under scrutiny and suffer from blind acceptance.
George Polya emphasizes the importance of critical thinking in the evaluation of ideas. Accepting ideas without question can lead to stagnation, while subjecting them to rigorous examination can enhance understanding and innovation.
In practice
During a team meeting, I reminded everyone that the best solutions come from questioning our assumptions.
Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.
If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
Mathematics is not a spectator sport!
Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
I would always advise young people to follow their star - not my star. They have to live their own life. If they decide they want to go into the investment business, do it, but make it a better business than it is today.
Seek the wisdom that will untie your knot. Seek the path that demands your whole being.
Young girls are sad. They like to be; it makes them feel strong.
Proper effort is not the effort to make something particular happen. It is the effort to be aware and awake each moment, the effort to overcome laziness and merit, the effort to make each activity of our day meditation.
The love of fame is the last weakness which even the wise resign.
Not to be able to stop thinking is a dreadful affliction, but we don't realize this because almost everyone is suffering from it, so it is considered normal. This incessant mental noise prevents you from finding that realm of inner stillness that is inseparable from Being.
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